# A kayak can travel 48 miles downstream in 8 hours, while it would take 24 hours to make the same trip upstream. Find the speed of the kayak in still​ water, as well as the speed of the current?

Mar 5, 2018

Still water kayak speed is 4miles/hr
Speed of current is 2miles/hr.

#### Explanation:

Assume speed of te kayak in still wate= k miles/hr
Assume speed of river current = c miles/hr

When going dwon stream : 48 miles in 8 hrs =6 miles/hr
When goinf up stream : 48 miles in 24hrs = 2miles/hr

When kayak is travelling downstream, the current helps the kayak,

$k + c = 6$

In reverse direction, kayak going against stream:

$k - c = 2$

$2 k = 8$

so $k = 4$

Substitute value for k in first equation:

$4 + c = 6$

So $c = 6 - 4$ = $2$

Still water kayak speed is 4miles/hr

Speed of current is 2miles/hr.